Structure and Dielectric Saturation of Water in Hydrated Polymer Electrolyte Membranes: Inclusion of the Internal Field Energy

Abstract

The nature of the water in hydrated polymer electrolyte membranes (PEMs) is distinct from that of bulk water and affects the rate of diffusion of protons in the material. Traditional methods used in the study of the phenomenon of dielectric saturation involve the assumption of the presence of a homogeneous or slowly varying external field, conditions that are hardly appropriate for PEMs. If the condition of field homogeneity is relaxed, a nonphysical divergence in the permittivity results. In this paper we show that through proper inclusion of the internal field energy the difficulty is rectified. Our recently derived equilibrium statistical mechanical model for the calculation of the spatial variation in the permittivity of water within PEMs has been extended to include the field energy. Using simple model calculations, we demonstrate that the interaction of the water molecules with the anionic sites constitute a more important contribution to the energy than the intermolecular forces. We have recalculated pore-radial profiles of the dielectric constant of the water in Nafion and 65% sulfonated PEEKK (poly arylene ether ketone) polymer electrolyte membranes over a range of hydration levels obtaining qualitative agreement with experiments. These profiles quantitatively show the increased ordering of the water in the neighborhood of the anionic sites, and although only the affect due to these sites is specifically computed, confinement effects on the water is implicitly included. In separate investigations, it was determined that both the uniformity in the distribution of the sulfonate groups, and the intrusion of these groups into the pore volume, will dramatically affect the permittivity of the water. Together our results help to elucidate the impact of structure and ordering of the water due to the effect of the fixed anionic groups on the underlying mechanisms of proton conduction in PEMs.